Towards a Rational Closure for Expressive Description Logics: the Case of 𝒮𝒽𝒾𝓆

Issue title: Special Issue on the 30th Italian Conference on Computational Logic: CILC 2015

Guest editors: Marco Maratea, Viviana Mascardi, Davide Ancona and Alberto Pettorossi

Article type: Research Article

Authors: Giordano, Laura^{a; *} | Gliozzi, Valentina^b | Olivetti, Nicola^c

Affiliations: [a] DISIT, Università del Piemonte Orientale “A. Avogadro”, viale Teresa Michel, 11 - 15121, Alessandria, Italy. laura.giordano@uniupo.it | [b] Dipartimento di Informatica, Università degli Studi di Torino, c.so Svizzera 185, 10145 Torino, Italy. valentina.gliozzi@unito.it | [c] Aix Marseille Univ, Universit de Toulon, CNRS, LIS, Marseille, France. nicola.olivetti@univ-amu.fr

Correspondence: [*] Address for correspondence: DISIT, Università del Piemonte Orientale “A. Avogadro”, viale Teresa Michel, 11 - 15121, Alessandria, Italy

Abstract: We explore the extension of the notion of rational closure to logics lacking the finite model property, considering the logic 𝒮𝒽𝒾𝓆. We provide a semantic characterization of rational closure in 𝒮𝒽𝒾𝓆 in terms of a preferential semantics, based on a finite rank characterization of minimal models. We show that the rational closure of a KB can be computed in EXPTIME based on a polynomial encoding of the rational extension of 𝒮𝒽𝒾𝓆 into entailment in 𝒮𝒽𝒾𝓆. We discuss the extension of rational closure to more expressive description logics.

Keywords: Description Logics, Nonmonotonic reasoning

DOI: 10.3233/FI-2018-1659

Journal: Fundamenta Informaticae, vol. 159, no. 1-2, pp. 95-122, 2018